# Power Factor Definition

**Power Factor** (PF) is the ratio between the energy that is converted into work and the electrical energy consumed in a circuit or device. In other words, power factor is the ratio between the total voltage applied to a circuit and the voltage in the resistive circuit part. PF is also:

- – Cosine of the angle (cos0) between the vectors of real power and apparent power.
- – Cosine of the angle (cos0) between impedance and resistance vectors.

The AC power, consumed by a circuit with resistive elements (resistors) and reactive elements (capacitors and / or inductors) can be obtained with the following formulas: P = I x V x PF or P = I_{RMS} V_{RMS} x PF

Notes:

- RMS means Root Mean Square
- PF = Power Factor

See the circuit above and the corresponding phasor diagram. Although the diagram represents an inductive value, the procedure is valid in general.

The current (I) and voltage (V_{R}) are in phase in the resistor R. The power (real power) dissipated in an impedance Z = (R + jX), is due only to resistance. Then: P = I x V_{R}

From the phasor diagram: V_{R} = V cos(0).

Combining the last two formulas we get: P = I x Vcos(0)

Comparing this equation with the expression: P = I x V x power factor, we conclude that: Power factor = cos (0). Where 0 is the phase angle of the impedance, or in other words, 0 is the angle between the voltage and current in the circuit.

Then PF = Cos(0) = V_{R}/V = R/|Z|

Where: |Z| means the absolute value of Z (Z value is always positive, regardless of the sign)

The angle value will always be between:

- 0 °: Where V and I are in phase (fully resistive circuit). Cos (0) = 1, then PF = 1
- 90: When V and I are 90 ° out of phase (fully reactive circuit). Cos (0) = 0, PF = 0

We seek to have a power factor as high as possible, where cos(0) tends to “1” (most resistive possible).